Since first introduced by Candes (Candes and T. Tao. Near optimal signal recovery from random projection: universal encoding strategies? IEEE Trans. on Information Theory, 52:5406-5425, 2006) and Donoho (D. L. Donoho. Compressed sensing. IEEE Trans. on Information Theory, 52:1289-1306, 2006), compressive sensing has been adopted in many applications to save sampling resources. Besides signal reconstruction, this technique has also been used in many different signal processing fields. Signal detection is also an important area for applying this technique and has shown strong advantage for detecting signals over very wide frequency band (See Xiangming Kong and Mohin Ahmed, “Quick signal detection and dynamic resource allocation scheme for ultra-wideband radar”, Proc. SPIE 8021, 802111 (2011)).
A detection scheme we previously developed (see U.S. patent application Ser. No. 13/091,020 (now U.S. Pat. No. 9,413,420) referred to above) has been shown to be able to track input signal S well when the input SNR is large and the signal dynamic range is moderate. However, when these conditions are not met, detections are missed and false alarm rate increases quickly. To overcome these shortcomings, a better detection scheme is proposed herein.